Related papers: Comparison of unknown unitary channels with multip…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
There have been many instances where the maximally entangled state as a probe acts better than the product and the non-maximally entangled states in the task of distinguishing quantum channels. We provide a proof that for single-shot…
We address the problem of unambiguously identifying the state of a probe qudit with the state of one of d reference qudits. The reference states are assumed pure and linearly independent but we have no knowledge of them. The state of the…
Suppose that three kinds of quantum systems are given in some unknown states $\ket f^{\otimes N}$, $\ket{g_1}^{\otimes K}$, and $\ket{g_2}^{\otimes K}$, and we want to decide which \textit{template} state $\ket{g_1}$ or $\ket{g_2}$, each…
Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be…
We investigate the simultaneous estimation of $n$ not necessarily identical unitary channels using multi-partite entanglement. We examine whether it is possible for the rate at which the mean square error decreases to be greater than that…
We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
Quantum channel discrimination is used to test quantum field theory in non-inertial frames. We search for optimal strategies which can best see the thermality of the Unruh effect. We find that the usual strategy of counting particles in the…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…
Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider a revised unambiguous discrimination of quantum resources. First, we present an upper bound of the success…
We address the question of a quantum memory storage of quantum dynamics. In particular, we design an optimal protocol for $N\to 1$ probabilistic storage-and-retrieval of unitary channels on $d$-dimensional quantum systems. If we may access…
Discrimination task is treated in the case of only partial prior information from measurements of unknown states. The construction of the optimal discrimination device and estimation of unknown states is performed simultaneously. A…
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are…